When the student moves the compressed coiled spring faster while keeping everything else the same, the characteristic that will increase is frequency.
Frequency refers to how many waves pass a given point in a certain amount of time. When the motion is made faster, more wave cycles occur in the same time period, resulting in an increase in frequency. Wavelength, on the other hand, would decrease if the speed of the wave increases while the wave speed remains constant.
So, the correct answer is frequency.